Winding formed from conductors of unequal length to reduce mechanical stresses



July 9. 1968 M. COTSAFTIS ET AL 3,392,356

. WINDING FORMED FROM CONDUCTORS OF UNEQUAL LENGTH TO REDUCE MECHANICAL STRESSES Filed Oct. 27, 1964 2 Sheets-Sheet 1 FlG/l INVENTORS MICHEL CansnFrls BRUNO LEON BY p/'RPE LEPOUX ATTORNEYS y 9. 1968 M. COTSAFTIS ET AL 3,392,356

WINDING FORMED FROM CONDUCTORS OF UNEQUAL LENGTH TO REDUCE MECHANICAL STRESSES Filed U012. 27, 1964 2 Sheets-Sheet, 2

FIG.2

INVENTORS M/cwa Consnrrrs Bewvo Leo/v BY PIERRE ZEROUX OM ATTORNEYS United States Patent 2 7 Claims. or. 336-180) The present invention relates to a method of reduction of mechanical stresses at the ends of a winding and a device for the practical application of said method.

A coil whose conductors carry an electric current generates an electromagnetic field within its internal volume. The conductors are accordingly subjected to electrodynamic stresses which result from the interaction of the field and the current. The said stresses are correspondingly higher as the density of said field is greater, and the mechanical stresses which said conductors are then called upon to withstand may result in the deformation and even the destruction of the winding.

A number of difierent experimental studies which are concerned especially with plasmas or ionized gases require a magnetic field of high density. This field is generated by a solenoid, each of the conductors of which, and particularly those which are located near the ends of the solenoid, are accordingly subjected to high mechanical stresses which limit the maximum value of the field which is generated.

It is known, however, that if a thin solenoid of infinite length were employed and the conductors of this latter were wound in a helix having an angular pitch equal to forty-five degrees, said solenoid would be free from any electrodynamic stress at all points. Such a solenoid of infinite length represents an ideal device which is of course impossible to produce in practice. However, it is not sufficient to adopt a solenoid whose length is great compared with its radius in order to practically cancel the stresses exerted on the solenoid conductors even on the assumption that these latter have been reduced in thickness since the limitation of such a solenoid, irrespective of its length, by two planes at right angles to its axis, produces electrodynamic stresses at all points of the winding which becomes higher towards the end planes. Certain windings of known types which are not rectilinear or limited at two ends but have the shape of a torus so as to generate fields of toroidal shape are, however, partially freed from mechanical stresses (Force Reduced Toroidal Systems, Wells and Mills High Magnetic Fields, published jointly by M.I.T. Press and John Wiley).

The present invention is directed to a method and arrangement which reduces the mechanical stresses at the ends of a winding, and which, accordingly, overcomes the disadvantages noted heretofore.

Said method and arrangement consist in making use of a coil having a number of conductors which are wound to define a cylinder having a radius R. The different conductors C C C carry currents 1 I I A transverse cross-sectional plane P cuts said coil along a circumference having a length L. The term density I per unit length is understood to mean the ratio:

a i=1 Ln of the sum of the amplitudes of the components I of the currents which pass through the transverse plane P to the length L.

3,392,356 Patented July 9, 1968 "ice The method according to the invention recommends the application of certain conditions to the aforesaid density I per unit length.

In accordance with this method, the conductors of a solenoid are arranged on a cylinder having a radius R so as to form one or a number of layers of helically wound conductors having an inclination to the direction of the generator-lines of said cylinder which is equal to an angle of 45 or an angle in the vicinity of this value, the current density J per unit length being constant.

The invention is characterized in that each end of said solenoid or so-called central solenoid is extended by a complementary solenoid of equal radius which is wound at the same angle of inclination to the direction of the generator-lines of the cylinder having a radius R, in that on the one hand the length of each complementary solenoid is between 1 and 10 times the radius of said central solenoid and that, on the other hand, the current density per unit length decreases progressively from the value thereof in the interior of the central solenoid to a zero value.

The said method is further characterized in that, I being the current density per unit length in the interior of one of the complementary solenoids having a length L and a radius R, and J being the value of said density per unit length in the interior of the central solenoid, the terminal position of the conductors of the complementary solenoids is so determined as to produce a decrease in the current density I per unit length as a function of the position L along the axis of said complementary solenoids as represented by a curve which is located within the domain defined by the following inequations:

The curve J=F(L) can either be continuous or have discontinuities, the amplitude of which is at the maximum equal to J 2.

This method makes it possible to reduce to an appreciable extent the electrodynamic stresses which are exerted on the conductors.

In order that the technical characteristics of the present invention may be more readily understood, there will now be described below one example of practical application thereof, it being understood that said example does not have any limitative character as far as any potential applications of the invention are concerned.

The constructional arrangements which will be described in connection with this example will be considered as forming part of the invention, it being understood that any equivalent arrangements can equally well be employed without thereby departing from the scope of the invention.

There are shown in the figures only those elements which are necessary for a proper understanding of the invention.

FIG. 1 represents a diagrammatic longitudinal view of the form of embodiment of a winding as constructed according to the method which forms the subject of this invention.

FIG. 2 is a graph on which is shown the curve representing the domain of the plane J-L as defined by the system of inequations 1-2-3 mentioned above as well as the profile J=F (L) of the complementary solenoid as represented in accordance with the invention.

FIG. 3 is a fragmentary view of an embodiment of the invention wherein multiple layers of windings are utilized.

In FIG. 1, a cylindrical core 1 of insulating material carries on the central portion thereof a winding 26, 27 constittuing the central solenoid in which only eleven conductors have been shown for the sake of convenience, said conductors being juxtaposed but electrically insulated from each other and uniformly disposed around the periphery of the core. It is only for the sake of clarity of the figure that the conductors are shown as spaced apart. The angle of inclination of the conductors with respect to the generator-line of the coil is equal to 45. In the vicinity of the two ends of the core 1, there are respectively disposed two groups of circular metallic end-plates 34 1213 and 3-4 12'- 13'. These end-plates are identical but not equidistant. It should be noted that those end-plates which are located at the right-hand extremity of the core and the corresponding end-plates which are located at the left-hand extremity have been designated by the same reference numerals to which is assigned the prime index in the second case.

The end-plates 3 and 13 at one end of the core and the end-plates 3' and 13' at the other end are spaced apart the same distances. Those portions of the core 1 which are occupied by said end-plates carry the so-called complementary windings. A first conductor 14 is connected at one end to the end-plate 3' and at the other end to the end-plate 3 which is joined to the end-plate 4' by means of a connection 15 which is parallel to the axis of the core 1. There is then connected to said end-plate 4 a second conductor 16 which is joined at the other end thereof to the end-plate 4. Said conductor 16 is wound around the core 1 next to the conductor 14.

A connection 17 which is parallel to the axis of the core 1 joins the end-plate 4 to the end-plate Said end plate 5' is electrically connected to the end-plate 5 by means of a third conductor 18 which is wound next to the second. The process of joining the different conductors to the corresponding end-plates is thus continued, the eleventh conductor 19 being connected to the last transverse end-plate 13. The said end-plate 13 as well as the first end-plate 3 are connected to a current supply source which has not been shown in the figure and which energizes the winding. The distances between the endplates are chosen so as to ensure that, said end-plates being joined to the conductors as herein-above described, the current density per unit length within the complementary windings accordingly decreases progressively from the value of said density within the central winding to a zero value.

The domain of the plane JL as defined by the Inequations 1 to 3 is represented in FIG. 2. This concerns the surface which is comprised within the hexagon defined by the straight-line segments 22-2344, a portion of the L-axis, a straight-line segment 25 and finally a portion of the J-axis. The straight-line segment 22 which is shown corresponds to the straight line J=J the straight-line segment 24 corresponds to the straight line L=1OB, the straight-line segment 23 is a portion of the straight line whereas the straight-line segment 25 corresponds to the According to the second characteristic feature of the method described, the curve J=F (L) which defines the profile of a complementary solenoid must be located within the hexagon which has already been defined.

The current density per unit length within this solenoid as a function of the length L is, for example, represented by the discontinuous curve 20 (as shown in FIG. 2) which consists of ten steps 2!. Eacls step corresponds to one portion of the complementary winding which is located between two consecutive end-plates and within which the density per unit length is constant.

The eleven conductors 2 which are wound in adjacent relation form one layer of the winding. The said winding is composed of p layers, as shown in FIGURE 3, which are identical with the preceding and uniformly arranged over the periphery of the core 1 in such a manner that the eleventh conductor of one layer is adjacent to the first conductor of the following layer. The corresponding conductors of the layers are connected in parallel to the corresponding metallic end-plates.

A first alternative form of the winding described above consists in dividing each metallic end-plate into N identical angular sectors which are electrically insulated from each other, each sector being designed to perform the function of an end-plate. It is thus possible to increase the number of layers of the winding and this latter can accordingly comprise a number of layers of superposed conductors. This alternative form proves advantageous to the adaptation of the impedances of the winding and of the current source, so that the different layers can be connected either in parallel, in series or in seriesparallel.

A second alternative form consists in dispensing with the end-plates or sectors and in bending the ends of the conductors at right angles to the axis of the core 1 at the same place as that in which said conductors had previously been soldered to said end-plates or sectors, said conductor-ends being accordingly extended along the radii of the core.

What we claim is:

1. An electrical coil winding of radius R and length L having reduced mechanical stresses at ends thereof, including;

a central solenoid portion comprised of a plurality of conductors helically wound in juxtaposed relationship with an axial pitch of about 45 degrees to form a predetermined number of layers of said central solenoid portion having a constant current density per unit length J said conductors being electrically extended at each end by a corresponding plurality of conductors comprising two complementary solenoid portions arranged, respectively, at the ends of said central solenoid portion;

the corresponding plurality of conductors comprising each said complementary solenoid portion being helically wound with an axial pitch of about 45 degrees and having lengths which vary progressively from one to ten times the radius R of said coil winding to form a plurality of composite conductors on said central and complementary solenoid portions which have unequal lengths terminated at progressively decreasing distances from said central solenoid portion; and

means for connecting said composite conductors in electrical circuit;

whereby the current density per unit length along said winding decreases progressively from the value J in said central solenoid portion to a zero value at the ends of said coil winding.

2. A coil winding as described in claim 1 wherein J is the current density per unit length in the interior of one of said complementary solenoids and the terminal position of the ends of said composite conductors is determined to cause a decrease in the current density per unit length as a function of the position L along the axis of said complementary solenoid which may be represented by a curve located within the domain of the plane J-L which is defined by the following inequations:

3. A coil winding as described in claim 2 wherein the curve J=F (L) is continuous.

4. A coil winding as described in claim 2 wherein the curve J=F(L) has discontinuities, the amplitude of which is, at the maximum, equal to 1 2.

5. A coil winding as described in claim 1 wherein the ends of the conductors of each said complementary solenoid portion are bent perpendicularly at the axis of the winding and oriented in the direction of the radii.

6. A coil winding as described in claim 1 wherein said central and complementary solenoid portions are wound on a cylinder upon which are disposed two groups of conductive end plates corresponding to said composite conductors;

said end plates being insulated from said cylinder and spaced symmetrically along said complementary solenoid portions, by progressively decreasing distances from said central solenoid portion, at locations which determine the terminal position of the ends of said composite conductors; and

means connecting the ends of each composite conductor, respectively, to corresponding end plates on either end of said cylinder.

7. A coil winding as described in claim 6 wherein said end plates are ring shaped and comprise a plurality of identical electrically isolated metallic sectors, the ends of said composite conductors located in the plane of one of said end plates each being joined to one of the sectors of said end plate.

References Cited UNITED STATES PATENTS 1/1924 Beard 336180 

1. AN ELECTRICAL COIL WINDING OF RADIUS R AND LENGTH L HAVING REDUCED MECHANICAL STRESSES AT ENDS THEREOF, INCLUDING; A CENTRAL SOLENOID PORTION COMPRISED OF A PLURALITY OF CONDUCTORS HELICALLY WOUND IN JUXTAPOSED RELATIONSHIP WITH AN AXIAL PITCH OF ABOUT 45 DEGREES TO FORM A PREDETERMINED NUMBER OF LAYERS OF SAID CENTRAL SOLENOID PORTION HAVING A CONSTANT CURRENT DENSITY PER UNIT LENGTH JO; SAID CONDUCTORS BEING ELECTRICALLY EXTENDED AT EACH END BY A CORRESPONDING PLURALITY OF CONDUCTORS COMPRISING TWO COMPLEMENTARY SOLENOID PORTIONS ARRANGED, RESPECTIVELY, AT THE ENDS OF SAID CENTRAL SOLENOID PORTION; THE CORRESPONDING PLURALITY OF CONDUCTORS COMPRISING EACH SAID COMPLEMENTARY SOLENOID PORTION BEING HELICALLY WOUND WITH AN AXIAL PITCH OF ABOUT 45 DEGREES AND HAVING LENGTHS WHICH VARY PROGRESSIVELY FROM ONE TO TEN TIMES THE RADIUS R OF SAID COIL WINDING TO FORM A PLURALITY OF COMPOSITE CONDUCTORS ON SAID CENTRAL AND COMPLEMENTARY SOLENOID PORTIONS WHICH HAVE UNEQUAL LENGTHS TERMINATED AT PROGRESSIVELY DECREASING DISTANCES FROM SAID CENTRAL SOLENOID PORTION; AND MEANS FOR CONNECTING SAID COMPOSITE CONDUCTORS IN ELECTRICAL CIRUIT; WHEREBY THE CURRENT DENSITY PER UNIT LENGTH ALONG SAID WINDING DECREASES PROGRESSIVELY FROM THE VALUE JO IN SAID CENTRAL SOLENOID PORTION TO A ZERO VALUE AT THE ENDS OF SAID COIL WINDING. 